The coefficient of x4 in the expansion of (1 - 2x)5 is equal to

Question

The coefficient of x4 in the expansion of (1 - 2x)5 is equal to (A) 40 (B) 320 (C) -320 (D) -32

Tardigrade Admin · Accepted Answer

General term of (1-2 x)5 is given by Tr+1 = 5 Cr(-2 x)r = 5 Cr(-2)r Xr For coefficient of x4, power of X=4 ∴ r=4 ∴ Coefficient of x4= 5 C4(-2)4 =5 × 16=80

Q. The coefficient of $x^{4}$ in the expansion of $(1 - 2 x)^{5}$ is equal to

40

320

-320

-32

80

General term of $(1 - 2 x)^{5}$ is given by
$T_{r + 1} =^{5} C_{r} (- 2 x)^{r}$
$=^{5} C_{r} (- 2)^{r} X^{r}$
For coefficient of $x^{4}$ , power of $X = 4$
$∴ r = 4$
$∴$ Coefficient of $x^{4} =^{5} C_{4} (- 2)^{4}$
$= 5 \times 16 = 80$

Q. The coefficient of x4 in the expansion of (1−2x)5 is equal to

40

320

-320

-32

80

General term of (1−2x)5 is given by Tr+1​=5Cr​(−2x)r =5Cr​(−2)rXr For coefficient of x4, power of X=4 ∴r=4 ∴ Coefficient of x4=5C4​(−2)4 =5×16=80

Q. The coefficient of $x^{4}$ in the expansion of $(1 - 2 x)^{5}$ is equal to

General term of $(1 - 2 x)^{5}$ is given by
$T_{r + 1} =^{5} C_{r} (- 2 x)^{r}$
$=^{5} C_{r} (- 2)^{r} X^{r}$
For coefficient of $x^{4}$ , power of $X = 4$
$∴ r = 4$
$∴$ Coefficient of $x^{4} =^{5} C_{4} (- 2)^{4}$
$= 5 \times 16 = 80$